The damping of ducted, fast, magnetohydrodynamic (MHD) waves by ion vi
scosity and electron heat conduction in a radiating, optically thin, w
arm, structured atmosphere has been evaluated. Dissipation is more eff
ective in a warm plasma than in a 'cold' one but, for waves ducted by
solar coronal loops, dissipation is only efficient if the periods of t
he waves are shorter than a few tens of seconds and only if the backgr
ound magnetic field is less than about 15 G. It appears that MHD waves
of longer periods and in stronger magnetic fields will survive the di
ssivative mechanisms considered here and may be manifest as observable
coronal oscillations.